The wooden darts had wooden shafts with real feather flights. The brass darts had shafts out of cane.
Now-a-days we've got shafts from different materials to screw in the barrels.
Usually all shafts and barrels will fit, the threads of the different manufacturers seem to match most if the time. That would mean should you for example use a Unicorn dart you don't have to use only Unicorn shafts, you can use more or less every shaft you like.
On the market you'll find cheap nylon shafts, a little bit more expensive aluminium shafts and, not so often, the rather expensive titanium shafts which are more durable then the rest.
You could say shafts are "articles of daily use" and not really expensive. They come as the barrels, in sets of three, but you can find economy-sized packages as well. Sometimes you can get shafts in sets of four - shafts are not really durable!!!
Aluminium shafts don't break at easy as the nylon shafts but they easily bend and then you can`t use them again. From the nylon shafts parts of the end where you stick the flights in, tend to break away but when you are not a beginner it doesn't happen too often. Sometimes nylon shafts break above the thread in the barrel and it can be a little bit tricky to get it out totally, but pocket-knives will do the trick most of the time.
Shafts you'll get in various colours and different lengths and there are different ways how to fix the flights. Most popular are the shafts in which you stick the flight at the end of the shaft but there exist side-loaded shafts as well.
You'll two different types of shafts: the locked ones and the "spinning" shafts. When you use spinning shafts the flights can spin away when another dart lands beside, which helps to reduce flight damage and opens more space.
As with the flights you should take the time to experiment a little bit with the shafts. You've to find out which setup you like best. Not every shaft/flight combination will work and with different shaft/flight combinations your dart will fly differently. Finding a good setup would mean that your darts land comparatively flat in the board and not with a big angle.
Unicorn offers a tool to find out a good Unicorn set-up for you the Unilab.
But though it might be in theory the ideal set-up you'll not necessarily feel comfortable with it and of course it only considers Unicorn products.
In the Darts Performance Centre shop you can buy an experiment pack by which you can try a lot of different flight/shaft combinations. That is a good way to find your ideal set-up. A review you can find here: Flight and Stems Experiment Pack